Question: Determine how many solutions exist for the system of equations. ${10x-2y = 4}$ ${10x-2y = 16}$
Convert both equations to slope-intercept form: ${10x-2y = 4}$ $10x{-10x} - 2y = 4{-10x}$ $-2y = 4-10x$ $y = -2+5x$ ${y = 5x-2}$ ${10x-2y = 16}$ $10x{-10x} - 2y = 16{-10x}$ $-2y = 16-10x$ $y = -8+5x$ ${y = 5x-8}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 5x-2}$ ${y = 5x-8}$ Both equations have the same slope with different y-intercepts. This means the equations are parallel. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ Parallel lines never intersect, thus there are NO SOLUTIONS.